Question

Find the Taylor series for $f(z)=\frac{i}{(z-i)(z-2i)}$ about $z_0=0$.

score 1.2k · Answer 1 · 2026-04-13 02:25:53

1.2k

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Find the Taylor series for $f(z)=\frac{i}{(z-i)(z-2i)}$ about $z_0=0$.

Published on 13 Apr 2026 - 2:25

score 91 · Answer 2 · 2026-04-14 18:16:33

91

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There is a relation between the eigenvectors of a matrix $A \in \text{SL}(2,\mathbb{R})$ and its transpose $A^T$?

Published on 14 Apr 2026 - 18:16

score 280 · Answer 3 · 2026-04-17 10:34:30

280

Views

For any complex $z$, $|z-1|\leq |z-j|+|z-j^2|$

Published on 17 Apr 2026 - 10:34

score 466 · Answer 4 · 2026-04-30 06:01:41

466

Views

Any generalization of the complex conjugates in the theory of fields?

Published on 30 Apr 2026 - 6:01

score 94 · Answer 5 · 2026-04-12 11:01:33

94

Views

Complex numbers limits

Published on 12 Apr 2026 - 11:01

score 172 · Answer 6 · 2026-03-26 06:26:03

172

Views

Finding the Locus if $z$ Purely Imaginary/Real

Published on 26 Mar 2026 - 6:26

score 265 · Answer 7 · 2026-04-24 19:18:37

265

Views

Finding "hidden" solutions to a simple complex system of linear equations

Published on 24 Apr 2026 - 19:18

score 920 · Answer 8 · 2026-04-11 22:15:00

920

Views

Using complex numbers to find reflections

Published on 11 Apr 2026 - 22:15

score 202 · Answer 9 · 2026-04-12 17:12:24

202

Views

Geometry question from IMO 2009

Published on 12 Apr 2026 - 17:12

score 204 · Answer 10 · 2026-05-16 06:08:32

204

Views

bilinear complex least squares method

Published on 16 May 2026 - 6:08

score 74 · Answer 11 · 2026-04-30 06:01:40

74

Views

Determinate the minimal polynomial of $\sqrt{a}$ where a is an algebraic complex number over $\mathbb{Q}$

Published on 30 Apr 2026 - 6:01

score 378 · Answer 12 · 2026-05-11 08:30:42

378

Views

If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines.... find the value of $|A|$.

Published on 11 May 2026 - 8:30

score 689 · Answer 13 · 2026-04-16 09:01:17

689

Views

Would a right triangle with bases $a=i$ and $b=1$ have hypotenuse $c=0$?

Published on 16 Apr 2026 - 9:01

score 99 · Answer 14 · 2026-04-25 04:49:55

99

Views

Finding all $z$ which satisfy $|\Re(z^2)| \equiv |\Re(z)|$ and $|\Im(z^2)| \equiv |\Im(z)|$

Published on 25 Apr 2026 - 4:49

score 251 · Answer 15 · 2026-04-11 16:01:43

251

Views

Use the sufficient conditions for differentiability to determine where the function $f(z) = e^{z^2}$ is differentiable

Published on 11 Apr 2026 - 16:01

List Question

Find the Taylor series for $f(z)=\frac{i}{(z-i)(z-2i)}$ about $z_0=0$.

There is a relation between the eigenvectors of a matrix $A \in \text{SL}(2,\mathbb{R})$ and its transpose $A^T$?

For any complex $z$, $|z-1|\leq |z-j|+|z-j^2|$

Any generalization of the complex conjugates in the theory of fields?

Complex numbers limits

Finding the Locus if $z$ Purely Imaginary/Real

Finding "hidden" solutions to a simple complex system of linear equations

Using complex numbers to find reflections

Geometry question from IMO 2009

bilinear complex least squares method

Determinate the minimal polynomial of $\sqrt{a}$ where a is an algebraic complex number over $\mathbb{Q}$

If $|z|^2+\bar{A}z^2+A(\bar{z})^2+B\bar{z}+\bar{B}z+c=0$ represents a pair of intersecting lines.... find the value of $|A|$.

Would a right triangle with bases $a=i$ and $b=1$ have hypotenuse $c=0$?

Finding all $z$ which satisfy $|\Re(z^2)| \equiv |\Re(z)|$ and $|\Im(z^2)| \equiv |\Im(z)|$

Use the sufficient conditions for differentiability to determine where the function $f(z) = e^{z^2}$ is differentiable

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